二值和三值自相关序列偶设计理论研究

发布时间：2018-04-28 01:37

本文选题：扩频序列设计 + 二进序列偶　；参考：《燕山大学》2014年博士论文

【摘要】：在扩频通信系统中，系统的抗干扰、抗截获、多址通信和同步等性能都与系统所采用扩频码的特性密切相关。因此，研究扩频序列设计理论、构造具有优良性能的扩频码，对提升现代扩频通信系统的性能具有重要的理论意义和实际价值。本课题针对现有序列偶扩频码存在空间小、低能量效率、相关性和平衡性差的问题，基于中国剩余定理、组合设计理论及交织序列理论，对扩频序列偶信号中的二值和三值自相关二进序列偶、二值和三值自相关四进序列偶和最佳高斯整数序列偶的构造法进行研究。首先，将组合设计理论与中国剩余定理理论相结合，提出一种新的基于指示序列和基序列的理想二值自相关二进序列偶构造方法；给出序列偶周期长度分别为(4m+3)(4m'+3)、(4m+1)(4m'+3)和(4m+1)(4m'+1)三种情况下，行序列应满足的条件；分析将四类典型理想二进制序列作为行序列情况下，所构造的序列偶在相关性、能量效率和平衡性方面的性能；通过改变所采用的的基序列和指示序列衍生出9种不同类型的理想二值自相关二进序列偶构造方法，进而根据二进序列偶与差集偶的等价关系，得到了9种新类型的差集偶。其次，在周期为4N的三值自相关二进序列偶构造方面，基于组合设计理论和交织序列理论，分别提出利用二阶分圆类和基于交织法的两种构造方法；在此基础上，通过定义不同的移位序列，衍生出3种周期为4N且旁瓣值为{0,-4}的三值自相关二进序列偶的构造方法，再根据三值自相关二进序列偶与几乎差集偶的等价关系，，得到9种新的几乎差集偶。针对奇数长三值自相关二进序列偶的构造问题，分别提出基于差集和基于差集偶的构造方法，研究所构造的序列偶在平衡性、相关性等方面的性能；为了解决偶数长最佳二进序列偶存在空间有限问题(仅存在峰值为4的一种类型序列偶)、突破奇数长二进制序列偶的相关函数值必须为奇数的限制，提出几乎二进制序列偶的概念，并基于二阶、四阶和六阶分圆类法、差集和差集偶法，提出几种几乎二进序列偶的构造方法；验证利用这些方法构造的(几乎)二进序列偶在相关性、平衡性和能量效率等方面的优越性。随后，研究周期为偶数的三值自相关四进序列偶的性质，并通过分析其最大旁瓣模值研究该类序列偶的相关性；利用逆Gray映射建立二进制序列偶与四进制序列偶之间的联系；提出一种势为N=2n1，特征序列偶为理想二值自相关二进序列偶，构造周期为N=4n2的三值自相关四进序列偶的新方法；利用交织法，通过取不同的移位序列，提出三种能满足这种相关特性的周期为偶数的三值自相关四进序列偶的构造方法，并分析这三种类型的三值自相关四进序列偶互不等价性。最后，利用逆Gray映射建立二进制阵列偶与四进制阵列偶之间的联系；为了扩大用来构造最佳四进阵列偶的基信号范围，从而得到更多的最佳四进阵列偶，提出利用周期互补二进阵列偶和最佳二进阵列偶构造最佳四进阵列偶的方法；提出利用最佳四进阵列偶和准最佳阵列偶或者几乎最佳四进阵列偶交替递归构造高阶最佳四进阵列偶的方法。为了拓展最佳高斯整数序列和最佳序列偶信号的存在范围，基于中国剩余定理理论和交织序列理论，提出利用奇数长最佳高斯整数序列构造奇合数长最佳高斯整数序列偶的方法；利用复数变换法和最佳屏蔽二进序列偶，提出几种得到偶数长最佳高斯整数序列偶的方法；研究同周期下，构造参数对所构造的最佳高斯整数序列偶等价性的影响。
[Abstract]:In the spread spectrum communication system, the performance of anti-interference, anti interception, multiple access communication and synchronization is closely related to the characteristics of the spread spectrum code used by the system. Therefore, it is of great theoretical and practical value to study the spread spectrum sequence design theory and construct the spread spectrum code with excellent performance. The problem of small space, low energy efficiency, correlation and poor balance exists in the existing sequence couple spread code. Based on the Chinese remainder theorem, combinatorial design theory and interleaving sequence theory, the two value and three value autocorrelation two entry pairs, two value and three value autocorrelation four entry pairs and the best Gauss integer in the spread spectrum sequence couple signal The structural method of sequence pairs is studied.
First, combining the theory of combinatorial design with the theory of Chinese remainder theorem, an ideal two value autocorrelation two progressive sequence pair construction method based on the sequence of instructions and the base sequence is proposed, and the conditions that the sequence pair periodic lengths are respectively (4m+3) (4m'+3), (4m+1) (4m'+3) and (4m+1) (4m'+1) are respectively satisfied. In the case of four typical ideal binary sequences, the performance of the sequence pairs in the aspects of correlation, energy efficiency and balance, and 9 different types of ideal two value autocorrelation two progressive sequence pairs are derived by changing the base sequence and the indication sequence, and then according to the two into the sequence couple and the difference. The equivalence relation of set pairs is obtained, and 9 new types of difference set pairs are obtained.
Secondly, based on the combination design theory and the interleaving sequence theory, based on the combination design theory and the interleaving sequence theory, the three values of the three value autocorrelation two progressive sequence are respectively based on the combination design theory and the interlacing sequence theory. On this basis, by defining different shift sequences, 3 cycles are derived from 4N and the sidelobe value is {0, and the three value of the -4} is self phase. The construction method of Guan Erjin sequence pairs is based on the equivalence relation between the three value autocorrelation two progressive sequence pairs and the almost difference set pairs. 9 new almost difference sets pairs are obtained. The construction method based on the difference set and the differential set pairs is proposed for the construction of the odd number of long three value autocorrelation two entry pairs. In order to solve the problem of the limited space of the best two progressive sequence pairs (only a type sequence pair with a peak of 4), the correlation function value of the odd long binary sequence pairs must be restricted by the odd number, and the concept of almost binary sequence pairs is proposed and based on the two order, the four order and the six order circle class. The method, the difference set and the differential set couple method are used to propose several construction methods of almost two progressive sequence pairs, and verify the superiority of the (almost) two input sequence pairs in the correlation, the balance and the energy efficiency.
Then, the study period is an even number of three value autocorrelation four entry pairs, and the correlation between the sequence pairs is studied by analyzing its maximum sidelobe modulus value, and the connection between binary sequence pairs and four sequence pairs is established by inverse Gray mapping. A potential is N=2n1, and the characteristic sequence pair is an ideal two value autocorrelation two order. The construction period is a new method of three value autocorrelation four entry sequence pairs of N=4n2. By using the interlacing method, by taking different shift sequences, the construction method of three kinds of three value autocorrelation four entry pairs, which can satisfy the periodic number of the correlation property, is proposed, and the three values of the three value autocorrelation four sequence pairs are not equivalent to each other. Sex.
Finally, the inverse Gray mapping is used to establish the relationship between binary array pairs and four array pairs. In order to expand the base signal range used to construct the best four input array pairs, the best four input array pairs are obtained, and the best method of constructing the best four input array pairs is proposed by using the periodic complementary two input array pairs and the best two input array pairs. In order to extend the existence range of the best Gauss integer sequence and the best sequence pair signal, the best Gauss integer sequence and the best four input array pair are constructed by using the best array pairs and the quasi optimal array pairs or the almost optimal four input array pairs. The Gauss integer sequence constructs the method of the best Gauss integer sequence pairs with the odd number of odd numbers. By using the complex number transformation method and the best shielded two entry sequence pair, several methods to obtain the best Gauss integer sequence pairs of the even number length are proposed, and the influence of the structural parameters on the optimal Gauss integer sequence pairs under the same period is studied.

【学位授予单位】：燕山大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN914.42

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